一类矩阵方程组的求解问题及其最佳逼近  

Solutions of a class matrix equations and its optimal approximation

作　　者：陈世军[1] 张凯院[1] 陈梅枝[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072

出　　处：《纺织高校基础科学学报》2008年第1期88-92,共5页Basic Sciences Journal of Textile Universities

基　　金：陕西省自然科学基金项目(2006A05)

摘　　要：对共轭梯度法进行适当变形,建立了求一类矩阵方程组AiXBi+CiXDi=Ei(i=1,2)的一般解的变形共轭梯度法.该迭代算法可以判断矩阵方程组解的存在性.在不考虑舍入误差时,对任意给定初始矩阵,该迭代算法能够在有限步迭代计算之后得到矩阵方程组的解;选取特殊的初始矩阵时可得到矩阵方程组的极小范数解.另外,在上述解集合中也可给出指定矩阵的最佳逼近矩阵.An iterative algorithm based on conjugate gradient method and its corresponding transforming form are introduced. It is presented to solve the common solution of the matrix equations AiXBi ＋CiXDi =Ei （i=1,2）. By this iterative method, the existence of the solutions can be determined automatically. When the equations are consistent, the solutions can be obtained within finite steps in the absence of round off errors , and the least-norm solution can be given by choosing a special initial matrix. In addition, its optimal approximation to a given matrix can be obtained in the solution set.

关 键 词：矩阵方程组 极小范数解 迭代算法 最佳逼近 

分 类 号：O241.6[理学—计算数学]